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Another elementary question regarding bounded sets and infimums

score 39 · Answer 1 · 2026-04-11 06:29:16

39

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Another elementary question regarding bounded sets and infimums

Published on 11 Apr 2026 - 6:29

score 2.3k · Answer 2 · 2026-04-16 00:33:37

2.3k

Views

IMO 1984: Prove that $0 ≤ yz + zx +xy −2xyz ≤ \frac {7}{27}$, where $x,y$ and $z$ are non-negative real numbers for which $x + y + z = 1.$

Published on 16 Apr 2026 - 0:33

score 63 · Answer 3 · 2026-05-11 08:56:28

63

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Standard inequality and Cauchy integral formula

Published on 11 May 2026 - 8:56

score 55 · Answer 4 · 2026-04-16 20:31:27

55

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Is the set $\left\{ \boldsymbol{\beta} \in \mathbb{R}^{p}: ||\mathbf{A} \boldsymbol{\beta} - \boldsymbol{d}|| \leq D \right\}$ compact?

Published on 16 Apr 2026 - 20:31

score 3.9k · Answer 5 · 2026-05-10 21:28:36

3.9k

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Proofs that the median and a 50th percentile aren't always the same thing. Is my reasoning correct?

Published on 10 May 2026 - 21:28

score 123 · Answer 6 · 2026-04-12 14:31:41

123

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Is this a valid solution to Putnam 2017 A3?

Published on 12 Apr 2026 - 14:31

score 50 · Answer 7 · 2026-04-16 15:54:41

50

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Proof: $z$ is a limit point of $(z_n)_{n\geq 1} \quad \iff \quad z$ is a limit point of $(z_n+w_n)_{n\geq 1}$

Published on 16 Apr 2026 - 15:54

score 82 · Answer 8 · 2026-04-11 16:09:28

82

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Are $m\mathbb{Z} \cong n\mathbb{Z}$ as rings for arbitrary $m,n \in \mathbb{N}$?

Published on 11 Apr 2026 - 16:09

score 62 · Answer 9 · 2026-05-11 05:36:10

62

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Compute $\oint_{\partial D_3(0)}\frac{\cos(z+4)}{z^2+1}dz$

Published on 11 May 2026 - 5:36

score 223 · Answer 10 · 2026-04-16 15:10:07

223

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Check my quick proof $P_1 \oplus P_2$ is projective $\iff P_1,P_2$ are projective.

Published on 16 Apr 2026 - 15:10

score 80 · Answer 11 · 2026-04-14 09:57:49

80

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Showing a set is compact in a different $\mathbb{R}^2$ topology

Published on 14 Apr 2026 - 9:57

score 236 · Answer 12 · 2026-04-16 23:40:05

236

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Suppose that $G$ is a group of order $924=2^2\cdot3\cdot7\cdot 11$. Prove that $G$ has an element of order $77$.

Published on 16 Apr 2026 - 23:40

score 429 · Answer 13 · 2026-04-15 05:53:40

429

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How to prove $\liminf\limits_{n\rightarrow \infty}(a_n+b_n)=\liminf\limits_{n\rightarrow \infty}a_n+\liminf\limits_{n\rightarrow \infty}b_n$

Published on 15 Apr 2026 - 5:53

score 57 · Answer 14 · 2026-04-14 11:59:26

57

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Basic Limits Proof (Calculus )

Published on 14 Apr 2026 - 11:59

score 44 · Answer 15 · 2026-04-11 06:34:35

44

Views

Is this homology sequence right?

Published on 11 Apr 2026 - 6:34

List Question

Another elementary question regarding bounded sets and infimums

IMO 1984: Prove that $0 ≤ yz + zx +xy −2xyz ≤ \frac {7}{27}$, where $x,y$ and $z$ are non-negative real numbers for which $x + y + z = 1.$

Standard inequality and Cauchy integral formula

Is the set $\left\{ \boldsymbol{\beta} \in \mathbb{R}^{p}: ||\mathbf{A} \boldsymbol{\beta} - \boldsymbol{d}|| \leq D \right\}$ compact?

Proofs that the median and a 50th percentile aren't always the same thing. Is my reasoning correct?

Is this a valid solution to Putnam 2017 A3?

Proof: $z$ is a limit point of $(z_n)_{n\geq 1} \quad \iff \quad z$ is a limit point of $(z_n+w_n)_{n\geq 1}$

Are $m\mathbb{Z} \cong n\mathbb{Z}$ as rings for arbitrary $m,n \in \mathbb{N}$?

Compute $\oint_{\partial D_3(0)}\frac{\cos(z+4)}{z^2+1}dz$

Check my quick proof $P_1 \oplus P_2$ is projective $\iff P_1,P_2$ are projective.

Showing a set is compact in a different $\mathbb{R}^2$ topology

Suppose that $G$ is a group of order $924=2^2\cdot3\cdot7\cdot 11$. Prove that $G$ has an element of order $77$.

How to prove $\liminf\limits_{n\rightarrow \infty}(a_n+b_n)=\liminf\limits_{n\rightarrow \infty}a_n+\liminf\limits_{n\rightarrow \infty}b_n$

Basic Limits Proof (Calculus )

Is this homology sequence right?

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